Overtwisted open books from sobering arcs

Abstract

We study open books on three manifolds which are compatible with an overtwisted contact structure. We show that the existence of certain arcs, called sobering arcs, is a sufficient condition for an open book to be overtwisted, and is necessary up to stabilization by positive Hopf-bands. Using these techniques we prove that some open books arising as the boundary of symplectic configurations are overtwisted, answering a question of Gay in Algebr. Geom. Topol. 3 (2003) 569--586.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-47.abs.html

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• On the stable equivalence of open books in three-manifolds
• Open books and configurations of symplectic surfaces and erratum

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• The topology and geometry of contact structures in dimension three
• A Note on Overtwisted Contact Structures
• A User's Guide to Morse Foliated Open Books
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